Gerrard reportedly turned down a chance to take over at English third-tier side Milton Keynes Dons after his playing contract with the Los Angeles Galaxy expired.
Carragher reckoned the chance to manage at Milton Keynes came too soon for his close friend, but added the 36-year-old former Liverpool and England skipper will move into coaching soon enough.
“I don't think that's going to happen now going there, I just don't think he fancies it (MK Dons),” Carragher said during a Twitter Q&A on Sky Sports' Monday Night Football show.
Steven Gerrard could rejoin Liverpool as an academy coach after he rejected the chance to manage Milton Keynes Dons. pic.twitter.com/wyL4IqXh9k— HotSports (@hotsportsng) November 22, 2016
“He's turned it down now but the fact he spoke to a club shows it will only be a matter of time.
“I just think it's come too early, six or 12 months down the line there would have been a good chance of it happening.
“I don't think he is fully ready yet. That's not to say he couldn't do the job, but maybe he wants to see if he can get more experience and he is still getting his coaching badges.”
Gerrard has not yet made any decision on his future, with Liverpool manager Jurgen Klopp having previously said there will always be a place for the Reds great at Anfield if he wants one.
But Carragher, now a television pundit, said it was credit to Gerrard that he wanted to go into coaching rather than the media.
“I think it's great he's making noises about going into management,” he added. “We've all been criticised for not going into that and going on TV, if you like.
“If he'd have taken the job it would have been a good decision in terms of the club. Alex Ferguson always used to say, 'Don't pick your club, pick your chairman'.
“That chairman (Pete Winkelman at MK Dons) gave Karl Robinson plenty of time, gave Roberto Di Matteo and Paul Ince a chance.
“I think the chairman more than the club probably would have enticed him.
“But he's only just got back from the States, his family didn't go over fully so it would be a big move to move down to Milton Keynes with the kids in school, that type of thing.”
Original source: Gerrard destined for management - Carragher